B Is angular momentum position specific?

Do we find out angular momentum for an object from a specific position? Since L= r x mv. R is the distance from the centre of mass. So can I say that angular momentum is 12 for a fixed position 4 metres away from centre of mass having mass of 1 kg and velocity of 3 metres per second north?

The angular momentum of the rigid body about a fixed point ##O## is calculated by the formula
##\boldsymbol L_O= m\boldsymbol{OS}\times \boldsymbol v_S+J_S\boldsymbol\omega##, here ##S## is the center of mass, ##m## is the mass of the rigid body, ##\boldsymbol v_S## is the velocity of the center of mass, ##J_S## is the operator of inertia about the center of mass, ##\boldsymbol\omega## is the angular velocity

Staff: Mentor

Do we find out angular momentum for an object from a specific position? Since L= r x mv. R is the distance from the centre of mass. So can I say that angular momentum is 12 for a fixed position 4 metres away from centre of mass having mass of 1 kg and velocity of 3 metres per second north?

Angular momentum is calculated around a given point, and the value you calculate may be different for different points.

Angular momentum is calculated around a given point, and the value you calculate may be different for different points.

That answers one part of the question. But nasu confused me. So can you tell me that the velocity is the velocity of centre of mass or of the particular point? I mean what is v in the formula L=r x mv?

The formula ##\mathbf{L}=\mathbf{r} \times m\mathbf{v}## is really for a point mass, so there is only one velocity.
But there is a similar formula for a rigid body
##\mathbf{L} = \mathbf{R}_{cm} \times M\mathbf{V}_{cm} + \overleftrightarrow{I}\mathbf{\omega}##
The first term is the orbital angular momentum, measured using the velocity of the center of mass, and the second term is the spin angular momentum (nothing to do with the quantum mechanics term). Basically, if it's not spinning, you can just treat the center of mass as a point particle.

Perhaps it helps to understand that an objects moment of inertia can depend on which axis it is being rotated about. For example a long thin rod will have a low moment of inertia when rotated about an axis that goes down the centre of the rod and a high moment of inertial when rotated about an axis through the middle of the rod. This is because mass further from the axis increases the moment of inertia more than mass close to the axis (think leverage).

I suggest reading up on how the moment if inertia is calculated for objects of different shapes. Basically you have to break the object down into small parts and then sum (integrate) the moment of inertia of all the component parts, each of which might be at a different radius from the axis of rotation.